Analysis and control of the motion of a rigid

							            Analysis and control of the motion of a rigid body
                      surrounded by a perfect fluid



                    Lionel ROSIER, Institut Elie Cartan (Nancy, France)

    In this talk we present some recent advances in the analysis and the control of fluid-rigid
body interactions. The fluid is assumed to be incompressible and perfect, and to fill an exterior
domain. Such a framework seems appropriate to capture the main features of fluid-structure
interactions for e.g. boats or submarines motions. In this framework, the motion of the fluid
(resp. the solid) is governed by the incompressible Euler equations (resp. the balance equations
for linear and angular momentum).
    In the first part of the talk we focus on the analysis of the complete system in 2D, without
any control. The main ingredients (vorticity estimates, velocity estimates) needed to prove the
existence and uniqueness of classical global solutions are presented ([1],[2]).
    In the second part we investigate the control of the position and velocity of the center of
mass of a ball surrounded by a potential fluid. The control of the system is the normal compo-
nent of the velocity of the fluid on a part of the boundary of the ball. Sharp conditions for the
exact controllability are provided [3].

[1] J. Ortega, L. Rosier, T. Takahashi, Classical solutions for the equations modeling the motion
of a ball in a bidimensional incompressible perfect fluid, ESAIM:M2AN, 39(1): 79–108, 2005.
[2] J. Ortega, L. Rosier, T. Takahashi, On the motion of a rigid body immersed in a bidimen-
sional perfect fluid, submitted.
[3] J. Ortega, L. Rosier, Control of the motion of a ball surrounded by an incompressible fluid,
in preparation.